Suppression of overflow limit cycles in LDI all-pass/lattice filters

Abstract

In this paper it is shown that zero-input overflow limit cycles can be suppressed in a class of lossless digital integrator (LDI) all-pass filters, namely, that introduced in [1]. This holds for any filter order, provided that saturation overflow characteristics are used at the input of each delay and for certain restrictions for the multiplier values. The results are shown to apply also to lossless digital differentiator (LDD) filters. The restrictions of multiplier values have the effect of excluding certain combinations of poles within the unit circle, most of which are in the left half circle where corresponding LDD filters can be used. Asymptotic stability can be guaranteed for all second-order LDI and LDD filters.